PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 463

R.5.12 The concept of causality is an important concept in many systems. Let us consider a

simple example where the output of a system depends only on the inputs f(n), f(n − 1),

f(n − 2), ..., f(n − k); and let the system equation be given by

gn fn fn fn k

k

() ()

1

2

(1)

1

2

 
 ()







The system block diagram is shown in Figure 5.5.

Its impulse response would then be given by

hn n n n n k

k

() ()

1

2

(1)

1

2

(2)

1

2

()

2


 

  
 
























and for k → ∞

hn n k un

k

k n

()

1

2

()

1

2

()

0



















∑ 

R.5.13 The output of a discrete-time system g(n) may depend on itself (the output sequ-

ence), which may be feedback into the system, as well as the input sequence f(n).

The following equation illustrates such a system:

gn gn f n()

1

2


 (1) ()







The system block diagram is shown in Figure 5.6.

FIGURE 5.5

System block diagram of R.5.12.

∑

Z–1

k delays

g(n)

f(n)

Z–1

Z–1

Z–1

1/2

1/2

1/2

1/2